Question

Computer output from a regression analysis is provided. Coefficients: Estimate Std. Error t value p-value (Intercept) 7.2960 14.5444 0.502 0.62200 X 1.6370 0.5453 3.002 0.00765 We want to do the hypothesis test to see if the slope in the population is different from zero? That is, do the hypothesis test to see if we have a statistically significant linear relationship. What is your decision on the hypothesis test and why? Use a level of significance of .05.

Answer 1

Answer:

Step-by-step explanation:

Hello!

You need to test the hypothesis that the slope of the regression is cero.

I've run in the statistic software the given data for Y and X and estimated the regression line:

Yi= 7.82 -1.60Xi

Where

a= 7.82

b=-1.60

Sb= 3.38

The hypothesis is:

H₀: β = 0

H₁: β ≠ 0

α: 0.05

This is a two-tailed test, the null hypothesis states that the slope of the regression is cero, this means that if the null hypothesis is true, there is no linear regression between Y and X.

The statistic for this test is a Student-t

t=  b - β   ~t$_{n-2}$

      Sb

The critical values are:

Left: $t_{n-2; \alpha /2} = t_{2; 0.025} = -4.303$

Right: $t_{n-2; \alpha /2} = t_{2; 0.975} = 4.303$

t= -1.60 - 0 = -0.47

      3.38

the p-value is also two-tailed, you can calculate it by hand:

P(t ≤ -0.47) + (1 - P(t ≤ 0.47) = 0.3423 + (1 - 0.6603) =0.6820

With the level of significance of 5%, the decision is to not reject the null hypothesis. This means that the slope of the regression is equal to cero, i.e. there is no linear regression between the two variables.

I hope this helps!